First, show deference to the "establishment." Show up on time, do your paperwork on time as required, and "play nice" with the site security team, even if they drool on their name badges. This will gain you the short-term trust of management. Bringing on new hires is always a headache for supervisors and managers. The less painful it is to deal with you, the more they will appreciate you. That should get you through the first week.
Second, figure out the "pecking order" in the team. Figure out who the "leader" is (it won't be who you were told) and ask them to give you the 1-2-3 of what's going on. Don't comment on anything you are told. If something is vague, ask for clarification, but do not judge either positively or negatively. Just learn. That will get the team to not see you as a disruptive "threat."
Third, do the tasks you are assigned. Ask for someone else to "look it over" before you do something that will disrupt another in the team for the first few weeks. If you are a software developer - that means have someone look at it before doing a commit on your code. If you're a network admin, have them "look over" your configuration changes before they are deployed. You'll pick up pretty quickly if "your way" fits with "their way." Again, don't judge, and don't try to change them. Learn and comply. Your chance to change things won't come until you build the trust up.
Finally, never, ever take credit for something you didn't do. That will ruin you. Never deny a mistake you made. Everyone expects "the new guy" to have a little trouble getting into the groove. If you do something that gets you publicly credited, publicly thank anyone who helped you, even if it was just borrowing a key to the server room. If your team knows helping you will help them, then your trust will start solidifying.
Of course, this is entirely dependent on what your role and department are. You should be able to glean the gist of this and "transpose" it to whatever your role is.
After that, you have to "read" the group and the individuals on your own. This will only get you going the right direction. After this, you will have to divine your own path.